"""
Water-Energy Nexus
For more details please refer to Chapter 10 (Gcode10.1), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
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Model type: MINLP
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Contributed by
Dr. Alireza Soroudi
IEEE Senior Member
email: alireza.soroudi@gmail.com
We do request that publications derived from the use of the developed GAMS code
explicitly acknowledge that fact by citing
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
DOI: doi.org/10.1007/978-3-319-62350-4
"""
from __future__ import annotations
import os
import pandas as pd
from gamspy import Container
from gamspy import Equation
from gamspy import Model
from gamspy import Parameter
from gamspy import Set
from gamspy import Sum
from gamspy import Variable
from gamspy.math import sqr
def reformat_df(dataframe):
return dataframe.reset_index().melt(
id_vars="index", var_name="Category", value_name="Value"
)
def data_records():
# gendata records table
cols = ["a", "b", "c", "Pmax", "Pmin"]
inds = [f"p{p}" for p in range(1, 5)]
data = [
[0.0002069, -0.1483, 57.11, 500, 0],
[0.0003232, -0.1854, 57.11, 400, 0],
[0.001065, -0.6026, 126.8, 400, 0],
[0.0004222, -0.2119, 57.11, 350, 0],
]
gendata_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))
# Coproduct records table
cols = [
"Pmax",
"Pmin",
"Wmax",
"Wmin",
"rmin",
"rmax",
"A11",
"A12",
"A22",
"b1",
"b2",
"C",
]
inds = [f"c{c}" for c in range(1, 4)]
data = [
[
800,
160,
200,
30,
4,
9,
0.0004433,
0.003546,
0.007093,
-1.106,
-4.426,
737.4,
],
[
600,
120,
150,
23,
4,
9,
0.0007881,
0.006305,
0.01261,
-1.475,
-5.901,
737.4,
],
[
400,
80,
100,
15,
4,
9,
0.001773,
0.01419,
0.02837,
-2.213,
-8.851,
737.4,
],
]
Coproduct_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))
# Waterdata records table
cols = ["a", "b", "c", "Wmax", "Wmin"]
inds = ["w1"]
data = [[1.82e-02, -7.081e-1, 7.374, 250, 0]]
waterdata_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))
# pwdata records table
cols = ["Pd", "water"]
inds = [f"t{t}" for t in range(1, 11)] + [f"t{t}" for t in range(16, 25)]
data = [
[1250, 150],
[1125, 130],
[875, 100],
[750, 150],
[950, 200],
[1440, 350],
[1500, 300],
[1750, 200],
[2000, 300],
[2250, 400],
[2500, 550],
[2125, 550],
[2375, 500],
[2250, 400],
[1975, 350],
[1750, 300],
[1625, 250],
[1500, 200],
[1376, 150],
]
pwdata_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))
return gendata_recs, Coproduct_recs, waterdata_recs, pwdata_recs
def main():
m = Container(delayed_execution=int(os.getenv("DELAYED_EXECUTION", False)))
# SETS #
t = Set(m, name="t", records=[f"t{t}" for t in range(1, 25)])
i = Set(m, name="i", records=[f"p{p}" for p in range(1, 5)])
c = Set(m, name="c", records=[f"c{c}" for c in range(1, 4)])
w = Set(m, name="w", records=["w1"])
# PARAMETERS #
gendata = Parameter(
m,
name="gendata",
domain=[i, "*"],
records=data_records()[0],
description="generator cost characteristics and limits",
)
Coproduct = Parameter(
m, name="Coproduct", domain=[c, "*"], records=data_records()[1]
)
waterdata = Parameter(
m, name="waterdata", domain=[w, "*"], records=data_records()[2]
)
PWdata = Parameter(
m, name="PWdata", domain=[t, "*"], records=data_records()[3]
)
# FREE VARIABLES #
of = Variable(m, name="of")
TC = Variable(m, name="TC")
CC = Variable(m, name="CC")
WaterCost = Variable(m, name="WaterCost")
# BINARY VARIABLES #
Up = Variable(m, name="Up", type="binary", domain=[i, t])
Uc = Variable(m, name="Uc", type="binary", domain=[c, t])
Uw = Variable(m, name="Uw", type="binary", domain=[w, t])
# POSITIVE VARIABLES #
p = Variable(m, name="p", type="positive", domain=[i, t])
Pc = Variable(m, name="Pc", type="positive", domain=[c, t])
Wc = Variable(m, name="Wc", type="positive", domain=[c, t])
Water = Variable(m, name="Water", type="positive", domain=[w, t])
p.up[i, t] = gendata[i, "Pmax"]
Pc.up[c, t] = Coproduct[c, "Pmax"]
Wc.up[c, t] = Coproduct[c, "Wmax"]
Water.up[w, t] = waterdata[w, "Wmax"]
# EQUATIONS #
costThermal = Equation(m, name="costThermal", type="regular")
balanceP = Equation(m, name="balanceP", type="regular", domain=[t])
balanceW = Equation(m, name="balanceW", type="regular", domain=[t])
costCoprodcalc = Equation(m, name="costCoprodcalc", type="regular")
Objective = Equation(m, name="Objective", type="regular")
costwatercalc = Equation(m, name="costwatercalc", type="regular")
ratio1 = Equation(m, name="ratio1", type="regular", domain=[c, t])
ratio2 = Equation(m, name="ratio2", type="regular", domain=[c, t])
eq1 = Equation(m, name="eq1", type="regular", domain=[w, t])
eq2 = Equation(m, name="eq2", type="regular", domain=[w, t])
eq3 = Equation(m, name="eq3", type="regular", domain=[c, t])
eq4 = Equation(m, name="eq4", type="regular", domain=[c, t])
eq5 = Equation(m, name="eq5", type="regular", domain=[c, t])
eq6 = Equation(m, name="eq6", type="regular", domain=[c, t])
eq7 = Equation(m, name="eq7", type="regular", domain=[i, t])
eq8 = Equation(m, name="eq8", type="regular", domain=[i, t])
costThermal[...] = TC == Sum(
[t, i],
gendata[i, "a"] * sqr(p[i, t])
+ gendata[i, "b"] * p[i, t]
+ gendata[i, "c"] * Up[i, t],
)
balanceP[t] = Sum(i, p[i, t]) + Sum(c, Pc[c, t]) == PWdata[t, "Pd"]
balanceW[t] = Sum(w, Water[w, t]) + Sum(c, Wc[c, t]) == PWdata[t, "water"]
costCoprodcalc[...] = CC == (
Sum(
[c, t],
Coproduct[c, "A11"] * sqr(Pc[c, t])
+ 2 * Coproduct[c, "A12"] * Pc[c, t] * Wc[c, t]
+ Coproduct[c, "A22"] * sqr(Wc[c, t])
+ Coproduct[c, "B1"] * Pc[c, t]
+ Coproduct[c, "B2"] * Wc[c, t]
+ Coproduct[c, "C"] * Uc[c, t],
)
)
costwatercalc[...] = WaterCost == Sum(
[t, w],
waterdata[w, "a"] * sqr(Water[w, t])
+ waterdata[w, "b"] * Water[w, t]
+ waterdata[w, "c"] * Uw[w, t],
)
Objective[...] = of == TC + CC + WaterCost
ratio1[c, t] = Pc[c, t] <= Wc[c, t] * Coproduct[c, "Rmax"]
ratio2[c, t] = Pc[c, t] >= Wc[c, t] * Coproduct[c, "Rmin"]
eq1[w, t] = Water[w, t] <= Uw[w, t] * waterdata[w, "Wmax"]
eq2[w, t] = Water[w, t] >= Uw[w, t] * waterdata[w, "Wmin"]
eq3[c, t] = Wc[c, t] <= Uc[c, t] * Coproduct[c, "Wmax"]
eq4[c, t] = Wc[c, t] >= Uc[c, t] * Coproduct[c, "Wmin"]
eq5[c, t] = Pc[c, t] <= Uc[c, t] * Coproduct[c, "Pmax"]
eq6[c, t] = Pc[c, t] >= Uc[c, t] * Coproduct[c, "Pmin"]
eq7[i, t] = p[i, t] <= Up[i, t] * gendata[i, "Pmax"]
eq8[i, t] = p[i, t] >= Up[i, t] * gendata[i, "Pmin"]
DEDcostbased = Model(
m,
name="DEDcostbased",
equations=m.getEquations(),
problem="minlp",
sense="min",
objective=of,
)
DEDcostbased.solve()
print("Objective Function Value: ", round(of.toValue(), 4))
if __name__ == "__main__":
main()
